Simplicial sheaf
Webb1 aug. 2015 · Stacks and the homotopy theory of simplicial sheaves. J. Jardine; Mathematics. 2001; Stacks are described as sheaves of groupoids G satisfying an eective descent condition, or equivalently such that the clas- sifying object BG satisÞes descent. The set of simplicial sheaf homotopy … Expand. 43. PDF. View 1 excerpt; Save. Webb8 jan. 2016 · Like a sheaf takes values in Set, a simplicial sheaf takes values in simplicial sets. What your lecturer was talking about was a sheaf (set-valued) defined on a …
Simplicial sheaf
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WebbContents Introduction 1 Simplicial and Singular Intersection Homology 2 Some Computations 4 Homology with Local Coe cients 6 Some Useful Properties of Intersection Homology 7 Sheaf-Theoretic Intersection Homology 8 INTERSECTION HOMOLOGY SIDDHARTH VENKATESH Abstract. WebbIs there a good way to define a sheaf over a simplicial set - i.e. as a functor from the diagram of the simplicial set to wherever the sheaf takes its values - in a way that while defined on simplex by simplex corresponds in some natural manner to what a sheaf over the geometric realization of the simplicial set would look like?
Webb15 sep. 2010 · Matthias Wendt. In this paper, we discuss the construction of classifying spaces of fibre sequences in model categories of simplicial sheaves. One construction proceeds via Brown representability and provides a classification in the pointed model category. The second construction is given by the classifying space of the monoid of …
WebbA simplicial sheaf (resp. simplicial presheaf) X is a simplicial object in the category of sheaves (resp. presheaves). In other words, Xis a con-travariant functor op!Shv(C), where … WebbSimplicial schemes. A simplicial scheme is a simplicial object in the category of schemes, see Simplicial, Definition 14.3.1. Recall that a simplicial scheme looks like. Here there …
Webbsimplicial sheaves of groups because we can check it at each point. Last, note that the de nition BG n = Gn only depended on the multiplication in G. In particular, we could do the …
WebbFor any pointed simplicial sheaf X in ∆opSh(Sm/k) one defines the A1-homotopy group sheaves, πA1 i(X), to be the sheaves of simplicial homotopy groups of a fibrant replacement of X in the A1-model structure. Morel, in his foundational work in [5, Ch. 6] has defined, for every integer i, A1-homology groups HA1 i(X) and canonical Hurewicz … fqshare githubWebbLet X be a finite simplicial complex. There is a well known linear algebra data description of (constructible with respect to the triangulation) sheaves of vector spaces on X. A … blairs hvacWebb22 feb. 2001 · On the other hand, given a cocycle * Theorem 7 is a generalization of Theorem 16 of [10], which deals with the case where G is a sheaf of groups and X is a … blair signs and safetyWebb8 jan. 2016 · Jan 8, 2016 at 19:46 Like a sheaf takes values in Set, a simplicial sheaf takes values in simplicial sets. What your lecturer was talking about was a sheaf (set-valued) defined on a simplicial set, which amounts to regarding the simplicial set as a topological space (via it's geometric realization). fq scythe\u0027sWebbBetter: A simplicial ring A • is a sheaf on Δ (the category of finite ordered sets endowed with the chaotic topology). Then a simplicial module over A • is just a sheaf of modules. … fqrm.ifWebbwhich is defined for any abelian sheaf A on the ´etale site for k. Here, L varies through the finite Galois extensions of k, and we write G = Gal(L/k) for the Galois group of such an extension L. Here, the scheme Sp(L) is the Zariski spectrum of the field L. The simplicial sheaf EG ×G Sp(L) is the Borel construction for the action of fq simplicity\u0027sWebb1 maj 2024 · In the introduction to his paper "Flasque Model Structures for Presheaves" (in fact simplicial presheaves) Isaksen states on the top of page 2 that his model structure has a nice characterisation of fibrant objects and that "This is entirely unlike the injective model structures, where there is no explicit description of the fibrant objects". fq sinew\u0027s